Not really much you can do with it cause it's all built and to take some of that thicker wood out will screw up all the dimensions. The ONLY possible solution I see is to take the ...I can't tell if it's a 2 x6 from the picture but take those out and replace them with two 2 x 2 piece with a 2" spacer in between. I hope I am explaining what I am thinking right but basically your slicing a two inch hole in that 2 x 6. It will make the railing seem much lighter and it wount be so overwhelming to look at since it will have a more airy feel to it....also I would go with color that more matches the house maybe something a touch darker so it gets more lost into the house and does not stand out so much

There are clear railing systems and/or you could have the wood rails cut out and put in smaller vertical pieces either wood or maybe metal?

What is the budget?

I think it looks fine; however the above specialists have made valuable suggestions. Important to work with someone who will not distort the look, but improve on it.

Here are some stainless steel cable railing examples.
http://www.houzz.com/ideabooks/4215726/thumbs/Deck-Cable-Railing-by-The-Cable-Connection